More than a thousand janitors marched through Back Bay on Saturday afternoon, cheering and waving signs after their union voted unanimously to authorize a strike.

If agreement on a new contract cannot be reached by Friday, the members of Service Employees International Union Local 32BJ may halt work, leaving most of the towering high-rise buildings above them and the subway system below without custodial staff.

“Nobody really wants to strike, but people are going to do what they need to for their families,” Dan Nicolai, a district leader for the union, said in the Back Bay Events Center before the vote began.

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The strike would affect 13,000 janitors, most of them immigrants, who clean 2,000 buildings, including the John Hancock, Prudential Tower, Vertex, and Biogen buildings. The janitors work in colleges, including Northeastern, Wentworth, Simmons, and New England Conservatory, as well as MBTA buildings and The Boston Globe, according to Eugenio Villasante, spokesman for the union.

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A spokesman for the Maintenance Contractors of New England, the group bargaining with the janitors’ union, said the vote to strike was unwarranted.

“We believe real progress was made on economic issues like wages and health care,” spokesman Matt Ellis said in the statement. “As a result, the MCNE believes today’s union strike vote is unnecessary.”

The union and the MCNE, which is an association of the 20 largest building service contractors in New England, held two days of “productive” talks last week, Ellis said.

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Villasante called janitors an “invisible workforce,” since most clean at night when people don’t see them.

But people do notice the results — and the absence — of janitors’ work, he said.

Jorge Rivera, an MBTA janitor for the past 11 years, pleaded with the energetic crowd to inform the union when they see violations in their workplaces.

“We come here, we get up, we do our jobs — the jobs that people don’t like to do,” he said shortly before the event began. On the Orange Line, he said, he picks up dirty needles and cleans elevators that people use as toilets.

But the MBTA laid off a portion of its custodial staff and recently reduced his hours from full time at 35 to part time at 25, causing him to lose his health insurance and making it difficult for him to make his condo payments, he said.

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Angel Rivera used to make $8 an hour in a nonunionized job, working overnight cleaning airplanes at Logan International Airport. He didn’t have enough money to pay rent and depended on food stamps, he said.

Now he makes $17.85 an hour, with health insurance, has 15 days of vacation, six sick days, and one personal day — and he still works at Logan, cleaning the interior of the airport for a unionized company, he said.

Elida Guevara, who earns $17.75 an hour cleaning offices in the John Hancock, said the wages and benefits, which include health insurance, allow her to provide for her 7- and 15-year-old daughters.

She intends to strike if necessary, she said.

Representatives for many of the affected buildings did not return e-mails seeking comment Saturday. A spokesman for the MBTA declined to comment on the impact of a potential strike.

The custodians say Greater Boston is enjoying low vacancy rates and sky-high rents and argue that a new contract should expand opportunities for full-time employment and ensure raises that keep up with the cost of living, the statement said.

The last contract the cleaners negotiated was shaped during a recession, the statement said, and economic conditions have since changed. The janitors’ proposals include expanding employer-paid health care to family members for full-time workers and a wage increase, the statement said.

Only 30 percent of the union’s janitors are currently full time, said Villasante.

Ellis said the MCNE has agreed to provide comprehensive family health coverage with no employee contribution for all full-time employees, instead of the current setup where employees contribute $280 per month toward family health insurance.

He said his group had also agreed to a wage increase, to increase employer contributions to the Pension and Training Funds, and to convert more positions to full time through the attrition of part-time employees.

“The MCNE is confident a fair and reasonable settlement can and will be reached without a strike,” said Ellis.

The union conducted a strike in 2002 that lasted four weeks, according to Nicolai. And though conditions have improved for janitorial staff over the years, the union and the contractors “are still far apart on some important issues,” he said.

Felix Arroyo, chief of health and human services for Boston, told the crowd in the auditorium before the vote that they had the support of Mayor Martin J. Walsh. Both he and the mayor come from immigrant families who struggled to provide a better life for their children, he said.

“I know what it means to not know if you can pay for your heat. I know what it means to bathe in cold water,” said Arroyo.

“The mayor has not forgotten where he came from,” he said, “and neither have I.”